Question

In an office, $30$% of the employees have scooters and $25$% have cars. Among those who have scooters, $90$% do not have cars. The probability that an employee has a car given that he does not have a scooter is

• A. $\frac{11}{35}$
• B. $\frac{33}{100}$
• C. $\frac{11}{50}$
• D. $\frac{9}{10}$

Answer 1

The correct option is C $\frac{11}{50}$

Let us assume that there are 100 employees in the office,

$\therefore$ $30$ members have scooters,

$25$ members have cars,

Among those who have scooters $27$ members do not have cars,

$P(S\cap \overline{C})=P(S\cup C)-P\left(C\right)$

Here $S$ represents event of selecting a member who has scooter,

$C$ represents the event of selecting the event of selecting a member having car,

$⟹P(S\cup C)=\frac{52}{100}$,

Required probability is $P(C\cap \overline{S})$,

$\therefore P(C\cap \overline{S})=P(C\cup S)-P\left(S\right)=\frac{52-30}{100}=\frac{11}{50}$